Question

In ΔABC, E is the mid-point of median AD such that BE produced meets AC at F. IF AC = 10.5 cm, then AF =

पर्याय

•  3 cm

• 3.5 cm

• 2.5 cm

•  5 cm

Answer 1

 ΔABC  is given with E as the mid-point of median AD.

Also, BE produced meets AC at F.

We have AC = 10. 5cm , then we need to find AF.

Through D draw DK || BF.

In ΔADK, E is the mid-point of AD and EF || DK.

Using the converse of mid-point theorem, we get:

 AF = FK…… (i)

In ,ΔBCFD is the mid-point of BC and BF || DK.

 KC = FK…… (ii)

From (i) and (ii),we have:

AF = FK , AF = KC…… (iii)

Now,

AC = AF +FK + KC

AC = AF + FK + KC

From (iii) equation, we get:

AC = AF + AF + AF 

AC = 3AF

` AF = 1/3 AC` …… (iv)

We have AC = 10.5cm .Putting this in equation (iv), we get:

`AF = 1/3(10.5cm)`

AF = 3.5cm

Hence the correct choice is (b).